{"id":"W1972167756","doi":"10.48550/arxiv.1102.2460","title":"Spectra of Symmetrized Shuffling Operators","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Conjugacy class; Combinatorics; Reflection group; Symmetric group; Conjecture; Operator (biology); Simplex; Spectrum (functional analysis); Discrete mathematics; Pure mathematics; Coxeter group; Coxeter element","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005274742,0.000413803,0.0003129492,0.001129779,0.0008173937,0.001334543,0.0004641112,0.0006233206,0.004410337],"category_scores_gemma":[0.0009098107,0.0002026499,0.0006170239,0.000396363,0.001913083,0.001665498,0.001086515,0.0007507667,0.0003843067],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007296765,"about_ca_system_score_gemma":0.0003864747,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004905038,"about_ca_topic_score_gemma":0.0003238984,"domain_scores_codex":[0.9995333,0.0000760269,0.00003225005,0.00009106773,0.0001412375,0.0001261799],"domain_scores_gemma":[0.9994732,0.0001265471,0.0001222201,0.00005723939,0.00005999706,0.000160748],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009213647,0.00004907735,0.000747072,0.00002766399,0.000004922159,0.0003779436,0.0005575059,0.001735957,0.01701649,0.974712,0.0004912947,0.004188031],"study_design_scores_gemma":[0.00005798856,0.0001810276,0.001791459,0.00002656612,0.000008839227,0.0008524803,0.0005506793,0.06519035,0.01382501,0.9148323,0.002621833,0.00006147682],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9312719,0.0001009675,0.05208138,0.0002514935,0.00006190723,0.00003405325,0.00008121657,0.0001572262,0.01595993],"genre_scores_gemma":[0.9853935,0.00005362499,0.009100402,0.0000731808,0.00005187332,0.00004412183,0.00006059888,0.00004700634,0.00517572],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004410337,"threshold_uncertainty_score":0.014754,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.166961997758775,"score_gpt":0.2329905850447019,"score_spread":0.06602858728592689,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}